A single photon emitted by a single particle in free space vacuum modes and its resonant interaction with two- and three-level absorbers

We consider the time-delayed coincidence counting of two photons emitted in a cascade by a single particle (atom, molecule, nucleus, etc). The time-dependence of the probability amplitude of the second photon in the cascade has a sharply rising leading edge due to the detection of the first photon, as results from causality. If a macroscopic ensemble of resonant two-level absorbers is placed in the path of the second photon between the radiation source and the detector, the photon absorption does not follow Beer's law due to the time-asymmetric shape of the photon. For very short delay times almost no absorption takes place, even in an optically dense medium. We analyze the propagation of such a second photon in a thick resonant three-level absorber if a narrow electromagnetically induced transparency (EIT) window is present at the center of the absorption line. It is shown that the EIT medium can change the asymmetric time dependence of the photon probability amplitude to a bell shape (EIT filtering). This bell-shaped photon interacts much more efficiently with an other ensemble of two-level absorbers chosen, for example, to store this photon and the information it carries.